Superluminal (but causal) propagation of wave packets in transparent media with inverted atomic populations

The propagation of limited-bandwidth signals, such as Gaussian wave packets, tuned to a transparent spectral region far below the resonance of an inverted two-level atomic medium, can be superluminal, i.e., with phase, group, and energy velocities all exceeding the vacuum speed of light c. Causality is not violated, however. Little distortion and gain can accompany this propagation.